Differential and Integral Equations

Modified motion by mean curvature: local existence and uniqueness and qualitative properties

A. Bonami, D. Hilhorst, and E. Logak

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We consider some free boundary problems involving motion by mean curvature and a nonlocal term. They arise as singular limits of various phase transition models. Using precise regularity estimates in Hölder spaces, we prove that these problems are well-posed. We study the qualitative behavior of the motion law and show in particular that the inclusion of interfaces is not preserved in time.

Article information

Differential Integral Equations, Volume 13, Number 10-12 (2000), 1371-1392.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35A07 35B65: Smoothness and regularity of solutions 35R35: Free boundary problems 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)


Bonami, A.; Hilhorst, D.; Logak, E. Modified motion by mean curvature: local existence and uniqueness and qualitative properties. Differential Integral Equations 13 (2000), no. 10-12, 1371--1392. https://projecteuclid.org/euclid.die/1356061130

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